In this paper, formulas for projection-type approximation functionals for quadratic minimal splines are obtained. The values of these functionals are used as coefficients in local approximation schemes. Examples of special cases of the resulting approximation structures, known to be quasi-interpolatory, are considered. Results of numerical experiments on approximating transcendental curves using the proposed local scheme are presented, and a numerical method for solving integral equations using projection-type functionals is developed. Bibliography: 21 titles.